Renormalized contact interaction in degenerate unitary Bose gases

Abstract

We renormalize the two-body contact interaction based on the exact solution of two interacting particles in a harmonic trap. This renormalization extends the validity of the contact interaction to large scattering lengths. We apply this renormalized interaction to a degenerate unitary Bose gas to study its stationary properties and elementary excitations using the mean-field theory and the hyperspherical method. Since the scattering length is no longer a relevant length scale at unitarity, universal properties are obtained that depend only on the average particle density. Our treatment shows that the universal relations for the total energy and for the two-body contact are $E/N=12.67{\hslash }^2⟨n^{2/3}⟩/2m$ and $C_2/N=11.8⟨n^{1/3}⟩$ respectively.

8 pages, 6 figures

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• Harmonically Trapped Four-Boson System
• Vortex lattice in the crossover of a Bose gas from weak coupling to unitarity
• Self-similarly corrected Pade approximants for nonlinear equations
• Weak-coupling to unitarity crossover in Bose-Fermi mixtures: Mixing-demixing and spontaneous symmetry breaking in trapped systems
• Hyperspherical-LOCV Approximation to Resonant BEC
• Two-Step Production of Resonant Bose-Einstein Condensates
• Hyperspherical approach to dipolar Bose-Einstein condensates beyond the mean-field limit